To hear Republican presidential primary candidates tell it, the federal workforce under President Obama has experienced ballooning job growth and huge wage increases. Such claims are a staple of Rep. Michele Bachmann’s (R-MN) stump speeches, and for months, former Massachusetts Gov. Mitt Romney (R) has promised to bring the rest of the workers’ pay into line with comparable employees in the private sector.

Speaking at the Koch brothers-backed Americans for Prosperity annual summit Friday, Romney repeated this pledge, saying the pay gap between public and private workers “must be corrected.” “Public servants shouldn’t get a better deal than the taxpayers they work for,” Romney added.

But if Romney truly wants to match the pay of public employees to that of private workers, he would have to give the federal workers a raise, according to a new report from the Bureau of Labor Statistics. And such a raise wouldn’t be a small one — according to the report, federal workers are underpaid compared to their private sector counterparts by an average of 26.3 percent, and that gap is widening, the Washington Post reports:

The federal government reported Friday that on average, its employees are underpaid by 26.3 percent compared with similar non-federal jobs, a “pay gap” that increased by about 2 percentage points over last year while federal salary rates were frozen.

When asked if, given the BLS report, Romney was promising to give federal workers a raise should he become president, a Romney campaign spokesperson sent ThinkProgress a report from the conservative Heritage Foundation that said federal workers “receive 30 to 40 percent more in compensation than private-sector employees” once wages and benefits were included. “The federal pay system gives the average federal employee hourly cash earnings 22 percent above the average private worker’s. Including benefits raises the average compensation disparity to between 30 and 40 percent,” James Sherk, the report’s author, wrote.

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The Project on Government Oversight (POGO) took an extensive look at the Heritage study, however, and found that it was riddled with errors and “methodological problems that call into question the validity of its findings and recommendations.” The Heritage study, for instance, used a BLS survey with a much smaller sample size than the one normally cited in such reports, leading to distortions in its analysis of federal worker pay. In fact, POGO found that the less reliable data distorted Heritage’s wage differentials by 21 to 146 percent.

The idea that federal workers are overpaid has become a favorite talking point of Republicans, and media outlets like the USA Today and conservative and libertarian think tanks have perpetuated the idea through reports littered with errors. As the most recent BLS report shows, however, those claims are baseless, and policies like federal pay freezes are only making pay disparities between the public and private sectors even worse.